Q: A rigid body rotates with an angular acceleration $$\alpha. $$Which kinematic equation gives its angular position $$\theta_f$$ after time $$\Delta t if $$its initial angular velocity is $$\omega_i$$ and initial position is $$\theta_i$$?

$$\theta_f = \theta_i + \omega_i \Delta t + \frac{1}{2} \alpha (\Delta t)^2$

Q: A disk rotates with a constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\omega_i$$ and it rotates through an angular displacement $$\Delta \theta$$, what is its final angular velocity $$\omega_f$$?

$$\omega_f^2$ = \omega_i^2$ + 2\alpha \Delta \theta$$

Question 1

A bicycle wheel is spinning at a constant angular velocity. If a small pebble is stuck at the rim and another at half the radius, which statement is true about their angular velocities?

Accepted Answer

Both pebbles have the same angular velocity.

Question 2

A fan blade rotates counterclockwise and is slowing down. What are the signs of its angular velocity $$\omega$$ and angular acceleration $$\alpha$$?

Accepted Answer

$$\omega is $$positive and $$\alpha is $$negative.

Question 3

Which equation correctly relates the linear speed $$v of a $$point on a rotating rigid body to its angular velocity $$\omega$$ and its distance $$r$$ from the axis of rotation?

Accepted Answer

$$v = r \omega$$

Question 4

A turntable rotates at a constant angular velocity. Coin A is placed at radius $$r$$ and coin B at radius $$2r. $$What is the ratio of their linear speeds $$v_A/v_B$$?

Accepted Answer

$$v_A/v_B = 1/2$$

Question 5

A rigid body rotates with an angular acceleration $$\alpha. $$Which kinematic equation gives its angular position $$	heta_f$$ after time $$\Delta t if $$its initial angular velocity is $$\omega_i$$ and initial position is $$	heta_i$$?

Accepted Answer

$$	heta_f = 	heta_i + \omega_i \Delta t + \frac{1}{2} \alpha (\Delta t)^2$

Question 6

A car wheel accelerates from rest with a constant angular acceleration $$\alpha. $$What is its angular velocity $$\omega$$ after time $$t$$?

Accepted Answer

$$\omega = \omega_i + \alpha t$$

Question 7

A spinning disk has an angular velocity $$\omega$$ and angular acceleration $$\alpha in $$the same direction. What happens to the disk's rotation?

Accepted Answer

The disk speeds up.

Question 8

Which of the following best describes the direction of the angular velocity vector $$\vec{\omega}$$ for a wheel rotating counterclockwise when viewed from above?

Accepted Answer

Upward, along the axis of rotation.

Question 9

A child spins a boomerang in the air. If the boomerang's angular velocity is increasing, what can be said about its angular acceleration?

Accepted Answer

Angular acceleration is positive.

Question 10

A particle moves in a circle of radius $$r$$ with constant angular velocity $$\omega. $$What is the magnitude of its centripetal acceleration $$a_c$$?

Accepted Answer

$$a_c = r \$$omega^2$$

Question 11

A rotating wheel has an angular velocity $$\omega$$ and a tangential acceleration $$a_t. $$What is the total acceleration $$a of a $$point on the rim?

Accepted Answer

$$a = \sqrt{a_t^2$ + a_c^2$}$$

Question 12

If the angular velocity $$\omega of a $$wheel is plotted versus time and the graph is a straight line with positive slope, what does the slope represent?

Accepted Answer

The angular acceleration.

Question 13

A disk rotates with a constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\omega_i$$ and it rotates through an angular displacement $$\Delta 	heta$$, what is its final angular velocity $$\omega_f$$?

Accepted Answer

$$\omega_f^2$ = \omega_i^2$ + 2\alpha \Delta 	heta$$

Question 14

A wheel completes 120 revolutions in 2 minutes. What is its frequency $$f in Hz$$?

Accepted Answer

$$f = 1 Hz$$

Question 15

A rigid body rotates with angular velocity $$\omega$$ and angular acceleration $$\alpha. $$Which equation gives the tangential acceleration $$a_t of a $$point at distance $$r$$ from the axis?

Accepted Answer

$$a_t = r \alpha$$

Question 16

A spinning top slows down due to friction. If its angular velocity is positive, what is the sign of its angular acceleration?

Accepted Answer

Negative

Question 17

Which of the following is NOT a property of a rigid body?

Accepted Answer

It can deform under rotation.

Question 18

A wheel rotates with a constant angular velocity $$\omega. $$What is the angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = 0$$

Question 19

A runner on a circular track of radius $$r$$ completes one lap in time $$T. $$What is the runner's angular velocity $$\omega$$?

Accepted Answer

$$\omega = 2\pi / T$$

Rotational Motion: Angular Kinematics and Dynamics

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